| FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS |
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| 引用本文： | CHENGDaizhan XIZairong. FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS[J]. 系统科学与复杂性, 2002, 15(1): 61-68 |
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| 作者姓名： | CHENGDaizhan XIZairong |
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| 作者单位： | Laboratory of Systems Science，Institute of Systems Science，Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | This research is supported partly by the National Natural Science Foundation of China(No.G59837270)and National 973 Project(No.G |
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| 摘 要： | 1 IntroductionIn the last few decades, symplectic geometry becomes a lbcus fOr multi-disciplines. Aspointed out in [1l: '"' cIassical mechanics, statistical mechanics, and quantum mechanics aretreated from the same perspective, that ofsylllplectic geornetry thus showing the unifying powerof the symp1ectic geometric approach." Particularly it becomes a new frame fOr Hamiltoniansystems[2--5]. Symp1ectic a1gorithm, [6] etc., provides a numerical method fOr solving the relatedproblems.In contr…
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FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS |
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| CHENG Daizhan,XI Zairong. FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS[J]. Journal of Systems Science and Complexity, 2002, 15(1): 61-68 |
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| Authors: | CHENG Daizhan XI Zairong |
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| Abstract: | This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output. Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given. For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered. |
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| Keywords: | Hamiltonianrealization symplectic group symplectic manifold Poisson bracket generalized Hamiltonian systems. |
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